Uni-GAUGE Syllabus 2018

Uni-GAUGE Syllabus 2018 - ERA foundation, the exam conducting body released Uni-GAUGE 2018 syllabus for Physics, Chemistry and Mathematics. Candidates who applied for the entrance exam need to refer the syllabus of Uni-GAUGE 2018 to prepare in a better way. The questions in the entrance exam were asked from the existing syllabus of class XI & XII or any equivalent exam. But, it was still important for candidates to refer to Uni-GAUGE syllabus 2018 as it was officially announced by the authorities and it also contained the topics and sub-topics of the subjects of the exam - Physics, Chemistry and Mathematics. The Uni-GAUGE 2018 syllabus was divided by candidates according to their convenience while preparing for the exam, in which, they were required to answer 180 questions. Candidates must know that for every correct answer in Uni-GAUGE, 1 mark will be awarded and there will be no negative marking for wrong answers in the exam. The complete syllabus of Uni-GAUGE 2018 can be checked by candidates from the full article given below.

Frame of reference, Motion in a straight line: Position-time graph, speed and velocity,Uniform and non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocity time and position-time graphs,Relations for uniformly accelerated motion (graphical treatment), Scalar and vector quantities; Position and displacement vectors, equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors. Relative velocity. Unit vector; Resolution of a vector in a plane - rectangular components. Scalar and Motion in a plane. Cases of uniform velocity and uniform acceleration-projectile motion. Uniform circular motion.

3

Laws of Motion

Intuitive concept of force. Inertia, Newton's first law of motion; momentum and Newton's second law of motion; impulse; Newton's third law of motion, Law of conservation of linear momentum and its applications, Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, lubrication, Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on banked road).

Centre of mass of a two-particle system, momentum conservation and centre of mass, Centre of mass of a rigid body; centre of mass of a uniform rod, Moment of a force, torque, angular momentum, laws of conservation of angular momentum and its applications, Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions, Moment of inertia, radius of gyration.Values of moments of inertia, for simple geometrical objects (no derivation). Statement of parallel and perpendicular axes theorems and their applications.

6

Gravitation

Keplar's laws of planetary motion.The universal law of gravitation, Acceleration due to gravity and its variation with altitude and depth, Gravitational potential energy and gravitational potential. Escape velocity. Orbital velocity of a satellite. Geo-stationary satellites.

Thermal equilibrium and definition of temperature (zeroth law of thermodynamics). Heat, work and internal energy. First law of thermodynamics. Isothermal and adiabatic processes, Second law of thermodynamics: reversible and irreversible processes. Heat engine and refrigerator.

9

Behaviour of Perfect Gases and Kinetic Theory of Gases

Equation of state of a perfect gas, work done in compressing a gas, Kinetic theory of gases - assumptions, concept of pressure. Kinetic interpretation of temperature; rms speed of gas molecules; degrees of freedom, law of equi-partition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path, Avogadro's number.

Electric Charges; Conservation of charge, Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field. Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside). Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graaff generator

2

Current Electricity

Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell,combination of cells in series and in parallel. Kirchhoff’s laws and simple applications. Wheatstone bridge, metre bridge. Potentiometer - principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell.

3

Magnetic Effects of Current and Magnetism

Concept of magnetic field, Oersted’s experiment. Biot - Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long straight wire. Straight and toroidal solenoids, Force on a moving charge in uniform magnetic and electric fields. Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity. Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements. Para-, dia- and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets

Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lensmaker’s formula. Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror. Refraction and dispersion of light through a prism. Scattering of light - blue colour of sky and reddish apprearance of the sun at sunrise and sunset. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying Powers. Wave optics: Wave front and Huygen's principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygen's principle. Interference Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum, microscopes and astronomical telescopes. Polarisation, plane polarised light Brewster's law, uses of plane polarised light and Polaroids.

a transistor, transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch

10

Communication Systems

Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave.

Introduction to Solid State Chemistry, Classification of Solids on the Basis of Order in the Arrangement, Crystal Lattices and Unit Cells, Close Packing in solids, Imperfections in Solids, Electrical Properties, Magnetic Properties

7

Solutions

Introduction to solutions, Types of Solutions, Expressing the Concentration of Solutions of Solids in Liquids, Solubility, Vapour Pressure of Liquid Solutions, Classification of Liquid-Liquid Solutions on the basis of Raoult’s Law, Colligative Properties, Abnormal Molecular Mass

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Uni-GAUGE Syllabus 2018 for Mathematics (Class XI)

S.No.

Units

Topics

1

Sets

Sets and their representations, Empty Set, Singleton Set, Finite and infinite Sets, Equivalent and Equal Sets, Subsets, Power Set, Universal Set, Complement of a Set, Intervals as Subsets of R, Venn diagrams, Union and Intersection of Sets, Difference of sets, Laws of Operations on Sets, Properties of Complement Sets, Practical Problems on union and Intersection of Sets

2

Relations and Functions

Ordered Pairs, Cartesian Product of Sets, Definition of Relation, Arrow Diagram, Domain, Codomain and Range of a Relation, Function as a Special Kind of Relation from one Set to another, Pictorial representation of a Function, Domain, Codomain and Range of a Function, Real valued functions and their graphs

3

Trigonometric

Functions

Positive and negative angles, Measuring angles in radians and in degrees and conversion from one measure to another, Definition of trigonometric functions with the help of unit circle, Sign of trigonometric functions, Domain and range of trigonometric functions, Trigonometric functions as periodic functions, their amplitude, argument, period and graph, Trigonometric functions of sum and difference of two angles, Express sum and difference of T-Functions as the product of T-ratios, Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x, General solution of trigonometric equations of the type sin = sin , cos = cos and tan = tan . finding general solutions of sin , cos = cos and tan = tan, Proof and simple applications of sine and cosine rules

4

Principle of Mathematical Induction

Process of proof by induction, Principle of mathematical induction and its applications

5

Complex Numbers and Quadratic Equations

Need for complex number, especially iota to be motivated by inability to solve some of quadratic equation, Standard form of complex number, Modulus and conjugate of complex number, Multiplication and division of complex numbers, Polar representation of complex number, Argand Plane, Statement of Fundamental theorem of algebra, Square root of a complex number, Solution of quadratic equations in the complex number system

6

Linear and Quadratic Inequalities

Linear inequations, Algebraic solutions of linear inequations in one variable, Algebraic solutions of linear inequations in two variables, Graphical solution of linear inequations in two variables, Inequations solving modulus functions

Pascal’s Triangle, History, statement and proof of the binomial theorems for positive integral indices, General and middle term in binomial expansion, Application of binomial theorem

9

Sequences and Series

Arithmetic Progression, Geometric Progression, Arithmetic mean, Geometric mean, Sum to n terms of an A.P., Sum to n terms of a G.P., Infinite G.P. and its sum, Relation between A.M. and G.M, Sum to n terms of special series, Arithmeticogeometric series, Harmonic Progression

10

Straight Lines

Brief recall of two dimensional geometry from earlier classes, Shifting of origin, Slope of a line, Angle between two lines, Various forms of equation of a line: parallel to axis, point slop form, slop intercept form, two point form, intercept form, and normal form, General equation of a line, Equation of family of lines passing through the point of intersection of two lines, Distance of a point from a line, Distance between parallel lines

Types of relations : reflexive, symmetric, transitive and equivalence relations, One to one and on to functions, Composite functions, Inverse of a function and binary operations, Concept of exponential and logarithmic function to the base, logarithmic function as inverse of exponential function and their graphs

Finding the areas of circles/ parabolas/ ellipses (in standard form only), Area bounded by a curve and a line, Area bounded between two curves

11

Differential

Equations

Definition, order and degree, General and particular solutions of a differential Equation, Formation of Differential equation, Homogenous differential equation of first order and first degree, Linear equation of first order, Applications of differential equation

12

Vectors

Vectors and Scalars, Magnitude and direction of a vector, Position vector of a point, Components of a vector, Addition of vectors, Properties of addition of vectors, Multiplication of a vector by a scalar, Position vector of a point dividing a line segment in a given ratio, Direction cosines and direction ratios of vector, Scalar (dot product) of Vectors, Projection of a vector on a number line, Vector Product, Scalar triple product

13

Three-dimensional Geometry

Brief recall of direction cosines and direction ratios of a line, Cartesian and vector equation of a straight line, Angle between two lines, Shortest distance between two lines, Distance between Parallel lines, Equation of a plane in normal form, Equation of a plane passing through a given point, Equation of plane in intercept Form, Equation of plane in General form, Equation of Plane through the intersection of two planes, Angle between two planes, Distance of a point from a plane, Image of a point in plane, Coplanar lines